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Volume and Angle Structures on 3-Manifolds

2007
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Asian Journal of Mathematics
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We propose an approach to find constant curvature metrics on triangulated closed 3-manifolds using a finite dimensional variational method whose energy function is the volume. The concept of an angle structure on a tetrahedron and on a triangulated closed 3-manifold is introduced following the work of Casson, Murakami and Rivin. It is proved by A. Kitaev and the author that any closed 3-manifold has a triangulation supporting an angle structure. The moduli space of all angle structures on a

doi:10.4310/ajm.2007.v11.n4.a2
fatcat:tdhsybafhnaa3fhshzxhxfjmki